Methods for metering two-phase flow

ABSTRACT

A method for metering two-phase flow wherein the successive accelerational pressure drops across an orifice plate and across a venturi coupled in series with the orifice plate are correlated to obtain one or more flow-rate parameter.

BACKGROUND OF THE INVENTION

The present invention pertains in general to methods for meteringtwo-phase flow and in particular to methods for metering two-phase flowusing an orifice plate and a venturi in series.

In an oil field in which steam injection is employed to enhance oilrecovery, each of a number of steam injectors may be fed by a branch ofa trunk line from a common steam generator. Due to flow-splittingphenomena at the branches, a different ratio of steam to total flow(steam plus water), also called steam quality, is likely to be presentin each branch.

A knowledge of the ratio of steam to total flow being injected in atwo-phase flow is critical to any understanding of the effects of steaminjection. Because it is impractical to predict this ratio from analysisof the injection apparatus, it is important to be able to determineflowrate parameters for calculating steam quality from measurements madeat each branch.

Many methods for metering single-phase flow, such as those dependentupon critical choke flow or those employing single orifice meters, losetheir accuracy when applied to a two-phase flow system. Other methods,such as steam calorimetry, have inherent sampling problems.

Two-phase flow may be metered by employing two or more measurementswhich are mathematically correlated.

One such approach involves the use of a gamma ray densitometer to makevoid fraction measurements and a turbine meter or drag disc to obtain asecond measurement. This approach is limited to a small quality rangeand requires the use of an expensive and delicate gamma ray densitometerinstrument.

In another such approach, exemplified by K. Sekoguchi et al, "Two-PhaseFlow Measurements with Orifice Couple in Horizontal Pipe Line", Bulletinof the ISME, Vol. 21, No. 162, December, 1978, pp. 1757-64, twosegmental orifices or baffles are coupled in series. The pressure dropacross each orifice or baffle is measured and correlated with thepressure drop across the other orifice or baffle. The orifices mustdiffer in configuration in order to provide independent measurements forthe purpose of correlation. One drawback of this approach is that datais not presented in dimensionless form suitable for predictingperformances for different systems.

Yet another such approach involves measurement of a frictional pressuredrop across a twisted tape, measurement of an accelerational pressuredrop across a venturi and correlation of the results. A disadvantage ofthis approach is that a very sensitive device is required to measure thepressure drop across the twisted tape.

Measurement of the pressure drops across a venturi and an orifice inseries may be done simply and at reasonable cost, as shown in D. Collinset al, "Measurement of Steam Quality in Two-phase Upflow with VenturiMeters and Orifice Plates", Journal of Basic Engineering, Transactionsof the ISME, March 1971. Although concurrent pressure drops weremeasured for calibration purposes in Collins et al, pp. 11-21, thepressure drops across an orifice plate and across a venturi coupled inseries have not previously been correlated for the purpose of meteringtwo-phase flow prior to the present invention.

SUMMARY OF THE INVENTION

Accordingly, the method of the present invention involves meteringtwo-phase flow in a pipeline including the following steps. A venturi isinstalled in the pipeline. An orifice plate is coupled in series withthe venturi in the pipeline and two-phase flow is introduced. Therespective accelerational pressure drops across the venturi and acrossthe orifice plate are measured and then correlated to obtain one or moretwo-phase flow flowrate parameters.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a view in diagrammatic partial cross-section of an apparatusfor practicing the method according to the present invention; and

FIG. 2 is a plot of the steam quality as calculated according to themethod of the present invention versus measured steam quality.

DESCRIPTION OF THE PREFERRED EMBODIMENT

As illustrated in FIG. 1, apparatus for practicing the method accordingto the present invention includes an orifice plate 20 having aconcentric orifice 25 within a portion of a steam pipeline 10. A venturi30 is coupled in series with orifice plate 20 so that the same two-phaseflow of steam and water passes through both in direction 15.

The accelerational pressure drop across orifice plate 20 is measured bymeans of pressure gauge 40 while the accelerational pressure drop acrossventuri 30 is measured by pressure gauge 50.

Steam pipelines and generators for two-phase steam flow are wellunderstood by those skilled in the art and will not be discussedfurther. Venturi 30 may be a standard Herschel venturimeter. Orificeplate 20 may be a sharp-edged orifice plate having a concentric orifice.Gauges 40 and 50 may be piezoelectric strain-gauges or mercurymanometers, for example.

According to a preferred embodiment of the present invention, two setsof calculations are correlated in order to obtain steam quality or flowrate. A first set of three equations is applied to the pressure dropacross venturi 30 while a second set of three equations is applied tothe pressure drop across orifice plate 20.

The first set of equations makes use of Martinelli's parameter 1/X asdefined by ##EQU1## where:

X=the steam quality;

ρ_(l) =the density of the liquid phase (water); and

ρ_(g) =the density of the gas phase (steam).

Martinelli's parameter is used to calculate the liquid pseudo-pressuredrop, Δp_(l), which is the pressure drop which would be recorded if theliquid phase were flowing as a single-phase fluid, so that ##EQU2##where: Δp=the measured two-phase pressure drop;

C=a correlation coefficient based upon calibration data; and all othervariables are as defined above.

The liquid pseudo-pressure drop is used to calculate the two-phase massflow rate, W, using the equation: ##EQU3## where: K=the appropriateorifice or venturi coefficient; and all other variables are as definedabove.

In the above set of equations, steam and water densities at giventemperature and pressures are readily available to those skilled in theart in tabular form. The correlation coefficient, C, is readilyobtainable for a given venturi or orifice by running calibration testson the orifice or venturi. The constant, K, may be calculated accordingto the American Gas Association Method as described in "Orifice Meteringof Natural Gas", American Gas Association Report No. 3, June, 1979.

The second set of calculations employs the parameter F_(p) modified fromRhodes et al, U.S. Pat. No. 4,312,234, at column 4, as: ##EQU4## where:D=the diameter of the orifice or venturi, and all other variables are asdefined above.

F_(p) is correlated as a function of steam quality, x, in the form:

    F.sub.p =ax.sup.b                                          (5)

where a and b are constants obtained by running calibration tests on aparticular orifice or venturi.

The total mass flow rate is then given by: ##EQU5## where all variablesare as defined above.

Accordingly, in order to predict quality and flow rate, equations(1)-(3) may be applied to orifice plate 20, for example, and equations(4)-(6) may be applied to venturi 30, for example. These two sets ofequations are solved for the two-phase flow rate, W. At the correctvalue for steam quality, x, the two-phase flow rates given by equations(3) and (6) should be equal.

EXAMPLE

Data was collected using an orifice plate having a 2-inch diameterorifice and a 2-inch internal diameter venturi tube in a 3-inch schedule80-pipe. Two-phase steam was introduced into the pipe.

Equations (1)-(3) were applied to venturi tube 30 and equations (4)-(6)were applied to orifice plate 20.

For venturi 30, ##EQU6##

For orifice plate 20,

    F.sub.p =1.396x.sup.0.871,                                 (9)

and

    W=2.87√ρ.sub.g Δpx.sup.-0.871             (10)

As illustrated by the open circles plotted in FIG. 3, the followingresults were obtained for steam quality:

    ______________________________________                                        Measured Quality                                                                             Predicted Quality                                              ______________________________________                                        0.75           0.78                                                           0.85           0.88                                                           0.75           0.68                                                           0.65           0.73                                                           0.82           0.78                                                           0.88           0.73                                                           0.77           0.73                                                           0.64           0.63                                                           0.77           0.68                                                           ______________________________________                                    

For comparison, equations (1)-(3) were applied to orifice plate 20 andequation (4)-(6) were applied to venturi 30 as follows:

For venturi 30,

    F.sub.p =1.058x.sup.1.128,                                 (11)

and

    W=3.78(√ρ.sub.g Δp)x.sup.-1.128           (12)

For orifice plate 20, ##EQU7##

As illustrated by the triangles plotted in FIG. 3, by applying equations(1)-(3) to orifice plate 20 and equations (4)-(6) to venturi 30, thefollowing results were obtained:

    ______________________________________                                        Measured Quality                                                                             Predicted Quality                                              ______________________________________                                        0.75           0.725                                                          0.85           0.675                                                          0.75           0.775                                                          0.65           0.775                                                          0.82           0.725                                                          0.88           0.775                                                          0.77           0.775                                                          0.64           0.623                                                          0.77           0.675                                                          ______________________________________                                    

One of the advantages of the method according to the present inventionis that venturi and orifice plates are very popular in flow metering andthus are easily obtainable and well understood. Also, only twoparameters are measured to predict flow rates as opposed to mosttechniques which require three parameters to be measured.

While the present invention has been described in terms of a preferredembodiment, further modifications and improvements will occur to thoseskilled in the art. For example, although metering of two-phase steamhas been described above, metering of any two-phase flow may be obtainedby employing the method according to the present invention.

I desire it to be understood, therefore, that this invention is notlimited to the particular form shown and that I intend in the appealedclaims to cover all such equivalent variations which come within thescope of the invention as claimed.

What is claimed is:
 1. A method for metering two-phase flow in apipeline comprising the steps of:installing a venturi in the pipeline;coupling an orifice plate in series with the venturi in the pipeline;introducing two-phase flow into the pipeline; measuring the two-phasepressure drop across the venturi; measuring the two-phase pressure dropacross the orifice plate; and correlating the two-phase pressure dropacross the venturi as determined by a first set of equations with thetwo-phase pressure drop across the orifice plate as determined by asecond set of equations to obtain one or more two-phase flow rateparameters, wherein said first set of equations comprises: ##EQU8## andwherein said second set of equations comprises: ##EQU9## where:1/X=Martinelli's parameter, x=quality, ρ_(l) =the density of a liquidphase, ρ_(g) =the density of a gaseous phase, Δp=the measured two-phasepressure drop across the device to which the equation is applied, C=acorrelation coefficient based upon calibration data, W=the two-phasemass-flow rate, K=an orifice coefficient for the venturi, F_(p) =a flowparameter, D=the diameter of the orifice, a=a first constant determinedfrom calibration data, and b=a second constant based on calibrationdata.
 2. A method for metering two-phase flow in a pipeline comprisingthe steps of:installing a venturi in the pipeline; coupling an orificeplate in series with the venturi in the pipeline; introducing two-phaseflow into the pipeline; measuring the two-phase pressure drop across theventuri; measuring the two-phase pressure drop across the orifice plate;and correlating the two-phase pressure drop across the venturi asdetermined by a first set of equations with the two-phase pressure dropacross the orifice plate as determined by a second set of equations toobtain one or more two-phase flow rate parameters, wherein said firstset of equations comprises: ##EQU10## and wherein said second set ofequations comprises: ##EQU11## where: 1/X=Martinelli's parameter,x=quality, ρ_(l) =the density of a liquid phase, ρ_(g) =the density of agaseous phase, Δp=the measured two-phase pressure drop across the deviceto which the equation is applied, C=a correlation coefficient based uponcalibration data, W=the two-phase mass-flow rate, K=an orificecoefficient for the orifice plate, F_(p) =a flow parameter, D=thediameter of the venturi, a=a first constant determined from calibrationdata, and b=a second constant based on calibration data.